Performance of efficient Minimization algorithms as Applied to Models of Peptides and Proteins
C. Baysal, H. Meirovitch and I.M.Navon
We test the effciency of three minimization algorithms as applied to models of peptides and proteins; they are, the limited memory quasi-Newton (L-BFGS) of Liu and Nocedal, the truncated Newton (TN) with automatic preconditioner of Nash, and the nonlinear conjugate gradients (CG) of Shanno and Phua. The molecules are modeled by two energy functions, one is the GROMOS87 united atoms force field defining the energy EGRO), which takes into account the intramolecular interactions only; the second is defined by the energy Etot = EGRO+Esolv where Esolv is an implicit solvation free energy term based on the solvent accessible surface area of the atoms. The molecules studied are cyclo-(D -Pro 1 -Ala 2 -Ala 3 -Ala 4 -Ala 5 ) (31 atoms), axinastatin 2 [cyclo-(Asn 1 - Pro 2 -Phe 3 -Val 4 -Leu 5 -Pro 6 -Val 7 ), 62 atoms], and the protein bovine pancreatic trypsin inhibitor (58 residues, 568 atoms). With EGRO, the performance of TN with respect to the CPU time is found to be 1.2 - 2 times better than that of both L-BFGS and CG, whereas with Etot, L-BFGS outperforms TN by a factor of 1.5 - 2.5, and CG by a larger factor. Still, the quality of the solution in terms of the value of the minimized energy and the gradient norm, obtained with TN, is always equivalent to or better than those obtained with L-BFGS and CG. The performance is analyzed in terms of criteria outlined by Nash and Nocedal. We find the distribution of the Hessian eigenvalues to be a reliable predictor of efficiency.
Keywords: energy minimization; cyclic peptides and proteins; implicit solvation models; truncated and quasi-Newton, Hessian eigenvalues.